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As intermediate quantities available from various existing numerical computations, the fluid Lagrangian time scales are of primary importance in the development of probability density function models for turbulent flows. Similarly, the time scales of the fluid seen by discrete particles in two-phase flows are essential for the development of dispersion models based on stochastic differential equations. Such time scales are obviously depending not only on the particle properties but also on the fluid Lagrangian and Eulerian time scales. A model is proposed here to estimate the directional dependence of the fluid Lagrangian time scales and drift coefficients in one-directional equilibrium turbulent shear flows, based on a local homogeneity assumption in the frame of the generalized Langevin model. Through comparison with available direct and large eddy simulation predictions in channel flows and in a homogeneous shear flow, the model is shown to lead to significant improvements in the streamwise and spanwis...

The purposes of the paper are twofold: (i) to present a rational approach to the modeling of inertial particle transport in anisotropic turbulent flows and (ii) to show how the anisotropy of fluid turbulence timescales affects the particle fluctuating velocities in homogeneous shear flow. For these purposes, the directional dependence of the Lagrangian autocorrelations of fluid velocities is incorporated into the statistical probability density function (PDF) model proposed previously. The anisotropic timescale (ATS) model is evaluated against numerical simulations for homogeneous shear turbulent flows and is compared to results predicted by the isotropic timescale (ITS) model. The new ATS model for the PDF of the particle velocity distribution in turbulent flow appears to yield slightly improved results over the ITS model.

The purposes of the paper are threefold: (i) to refine the statistical model of preferential particle concentration in isotropic turbulence that was previously proposed by Zaichik and Alipchenkov [Phys. Fluids 15, 1776 (2003)], (ii) to investigate the effect of clustering of low-inertia particles using the refined model, and (iii) to advance a simple model for predicting the collision rate of aerosol particles. The model developed is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of particle pairs. Improvements in predicting the preferential concentration of low-inertia particles are attained due to refining the description of the turbulent velocity field of the carrier fluid by including a difference between the time scales of the of strain and rotation rate correlations. The refined model results in a better agreement with direct numerical simulations for aerosol particles.

This paper presents two statistical models for predicting collision rates of bidisperse heavy particles suspended in homogeneous isotropic turbulence. One of the models is based on the assumption that the joint fluid-particle velocity distribution function is Gaussian. The other model stems from a kinetic equation for the two-point probability density function of the velocity distributions of two particles. The validity of these models is tested against DNS data by Zhou, Wexler, and Wang [J. Fluid Mech. 433, 77 (2001)]. Comparisons between the model predictions and DNS results demonstrate encouraging agreement.

The objective of the paper is to present a statistical model for predicting pair dispersion and preferential concentration of particles suspended in an isotropic homogeneous turbulent flow field. This model is based on a kinetic equation for the probability density function of the relative velocities of two particles. The model developed is applied to predict the pair relative velocity statistics and the accumulation effect of heavy particles in a steady-state suspension. The effect of particle inertia on the predicted Eulerian two-point particle velocity correlations is demonstrated and compared with known results of numerical simulation.

The objective of the paper is to present and compare two models for the collision rate of inertial particles immersed in homogeneous isotropic turbulence. The merits and demerits of several known collision models are discussed. One of the models proposed in the paper is based on the assumption that the velocities of the fluid and a particle obey a correlated Gaussian distribution. The other model stems from a kinetic equation for the probability density function of the relative velocity distribution of two particles. The predictions obtained by means of these two models are compared with numerical simulations published in the literature.